tracking user from external site ?user= rewriting URL

I am quite a novice with php so please have some patience with me. I have a site that I administer which is going to be integrating with another outside site. I need to track and pass on through URL users that have logged into the external site and are brought to my site. Their login name needs to be added to all pages as they traverse my site, and bring it with them when they leave again. All my pages are already php pages mostly just so I can use php includes for the navigation. I have heard about using hidden form fields to do this but I really have no idea how. The webmaster of the external site has no patience for me and just wants to make me look bad, so I really want to get this working (with your help). All my navigation is in one navigation.php file and one .js file for the drop menus. I just don't know where to start, and I don't want to build a huge additional script to do it if possible.

I need to pass on ?user=userloginname through the whole site. Do I use a hidden field somehow, and if so how exactly?